Question

How do I find the domain of f(x, y) =4-x^2-2y^2

Answer 1

\[\large f(x, y) =4-x^{2}-2y^{2} \]

Answer 2

i know how to do it when there are fractions and the denominator cannot equal 0 or the natural logarithm of something most be greater than zero but dont have any restrictions on this one so not sure what to do. @hartnn

Answer 3

Perhaps the simplest way is to consider a 2D section (contour map).

So u set f(x,y) = constant c (if c is 0 y have an ellipse, then vary c up and down, see what happens)

Answer 4

i would say since x is not restriced because of any square root sign or denominator, the domain is all real numbers.....

Answer 5

*restricted

Answer 6

this is a polynomial. the domain for a polynomial is not restricted. Therefore the domain is \(\mathbb{R}\times\mathbb{R}\)